Bresenham's Line Drawing Research Articles

Clock Skew Compensation Algorithm Immune to Floating-Point Precision Loss

We propose a novel clock skew compensation algorithm based on Bresenham's line drawing algorithm. The proposed algorithm can avoid the effect of limited floating-point precision (e.g., 32-bit single precision) on clock skew compensation and thereby provide high-precision time synchronization even with resource-constrained sensor nodes in wireless sensor networks.

Bresenham's Line and Circle Drawing Algorithm using FPGA

In Bresenham's line drawing algorithm, the points of an n-dimensional raster that have to be selected are determined forming a close approximation to a straight line existed between two points. It is widely used for drawing line primitives in a bitmap image (for example: on a computer screen), since only integer addition, subtraction and bit shifting are used. These three operations are cheap concerning standard computer architectures. In addition, it is an incremental error algorithm. It is among the oldest algorithms that have been developed in computer graphics. An extension to the original algorithm may lead to draw circles. This research deals with the Bresenham’s line and circle drawing algorithm based on FPGA hardware platform. The shapes on the VGA screen are displayed via internal VGA port that is built in the device.

POLYGONAL APPROXIMATION OF DIGITAL CURVE BASED ON REVERSE ENGINEERING CONCEPT

This paper applies reverse engineering on the Bresenham's line drawing algorithm [J. E. Bresenham, IBM System Journal, 4, 106–111 (1965)] for polygonal approximation of digital curve. The proposed method has a number of features, namely, it is sequential and runs in linear time, produces symmetric approximation from symmetric digital curve, is an automatic algorithm and the approximating polygon has the least non-zero approximation error as compared to other algorithms.

LEARNING HOW TO DESIGN A GRAPHICS PROCESSOR

This paper describes the design and implementation of a rudimentary graphics processor, called GRAFIX, intended for use in a simple handheld gaming console. The processor is a part of a laboratory in an undergraduate course on Digital Systems Design 2 (DSD2) [1-2]. The GRAFIX processor can perform two different operations: (a) drawing an individual pixel, and (b) drawing a line using the Bresenham line drawing algorithm.The DSD2 course provides foundational material on discrete mathematics and the theory of modern very-large switching circuits. It presents computer engineering students with a firm foundation in the modern theory of optimal logic design. It illustrates some applications through formal characterization of combiniational functions and sequential machines, using contemporary techniques for the automatic synthesis and diagnosis of digital systems. It discusses (i) the design of VLSI systems with problems and approaches; (ii) gound-up development of algebraic structures, lattices, Boolean algebras for a generalized switching theory; (iii) exact optimization of two-level switching functions; (iv) heuristic techniques for the optimization of two-level logic circuits; (v) analysis, synthesis and optimization of complemented binary decision diagrams (BDDs) [3]; and (vi) provides design examples throughout the course.This fairly high-level lab design of a graphics processor is possible because the students have acquired the necessary prerequisite knowledge from previous courses. None of the courses, however, has attempted to develop a complete processor of such scale. The machine specifications include: (a) interfacing of the host to the GRAFIX unit may be synchronous or asynchronous (one must be selected and the consequences of the choice must be discussed); (b) the frame buffer can be either a single port memory or a dual port memory (again, one must be selected, and the consequences of the choice must be discussed); (c) interfacing of the GRAFIX unit to the frame buffer may be synchronous or asynchronous. The GRAFIX lab is split into four sessions: (i) familiarization with tools and design of the arithmetic logic unit (ALU) for GRAFIX, (ii) design of its Data Path Unit (DPU), (iii) design of its Computing Control Unit (CCU), and (iv) integration and testing.The objectives of those sessions are to learn how to (a) formulate an architecture of a simple graphics processor, (b) formulate an appropriate ALU, (c) formulate a DPU and CCU, (d) formulate a Command Interpreter, (e) formulate an Controller/Sequencer, (f) formulate the CCU interfacing with the GRAFIX I/O and with the DPU, (g) construct test procedures for each unit and incremental testing, (h) construct a supervisory module to provide the completed GRAFIX processor with test input, (i) integrate the system, (j) test operation of the GRAFIX processor, and (k) describe the system. VERILOG is used as the hardware-description language of choice.The paper provides a detailed description of the architecture of the graphics processor, its design and implementation, as well as experience from running the laboratory many times.

Line Drawing Algorithm on an Interleaved Grid

paper Bresenham's line drawing algorithm on interleaved grid is proposed. It uses the advantages of interleaved sampling to scan-convert the pixel on the raster with less representation error. The performance of the proposed algorithm is compared with the conventional Bresenham's algorithm on square grid. The qualitative and quantitative analyses show that the proposed algorithm outperforms the Bresenham's line drawing algorithm on square grid.

From program verification to program synthesis

This paper describes a novel technique for the synthesis of imperative programs. Automated program synthesis has the potential to make programming and the design of systems easier by allowing programs to be specified at a higher-level than executable code. In our approach, which we call proof-theoretic synthesis, the user provides an input-output functional specification, a description of the atomic operations in the programming language, and a specification of the synthesized program's looping structure, allowed stack space, and bound on usage of certain operations. Our technique synthesizes a program, if there exists one, that meets the input-output specification and uses only the given resources. The insight behind our approach is to interpret program synthesis as generalized program verification, which allows us to bring verification tools and techniques to program synthesis. Our synthesis algorithm works by creating a program with unknown statements, guards, inductive invariants, and ranking functions. It then generates constraints that relate the unknowns and enforces three kinds of requirements: partial correctness, loop termination, and well-formedness conditions on program guards. We formalize the requirements that program verification tools must meet to solve these constraint and use tools from prior work as our synthesizers. We demonstrate the feasibility of the proposed approach by synthesizing programs in three different domains: arithmetic, sorting, and dynamic programming. Using verification tools that we previously built in the VS3 project we are able to synthesize programs for complicated arithmetic algorithms including Strassen's matrix multiplication and Bresenham's line drawing; several sorting algorithms; and several dynamic programming algorithms. For these programs, the median time for synthesis is 14 seconds, and the ratio of synthesis to verification time ranges between 1x to 92x (with an median of 7x), illustrating the potential of the approach.

Drawing lines by uniform packing

In this paper, we introduce a new approach to line drawing that attempts to maintain a uniform packing density of horizontal segments to diagonal segments throughout the line. While the conventional line drawing algorithms perform linear time computations to find the location of the pixels, our algorithm takes logarithmic time. Also, experimental results show that the quality of line is acceptable and comparable to the well-known Bresenham's line-drawing algorithm.

Selections from the SIGGRAPH 96 educator's program

We are developing a suite of interactive modules for teaching introductory computer graphics, using a library we have built to support such efforts.The modules provide explanations of fundamental concepts, tutorial demonstrations of basic techniques and interactive control or the parameters used in and execution of high level representations of elementary algorithms. The modules are used in laboratory sessions to supplement format lectures. Here, we present our philosophy in building the library and modules, discuss the lessons we have learned in our initial implementation and outline our fur,,re plans. Introduction Computer graphics is, by its very nature, highly visual.To supplement traditional teaching aids such as whiteboards and overhead projectors, 35ram slides and videotape segments can be used to illustrate relevant concepts. However, for students to appreciate fully both the algorithmic and visual aspects of the fundamental topics presented in an introductory computer graphics course, it is usually necessary for them to implemenr the various algorithms introduced. We are creating a suite of inrerective modules that both present the fundamental computer graphics concepts and algorithms and allow students to manipulate the principal variables involved. This approach not only obviates the need for students to reinvent the wheel w i~ a lot of tedious programmir~ but also allows them to explore many more of the basic concepts than is possible co cover in great detail in class presentations or programming assignments. Previous work has focused on using computer graphics to visualize algorithm execution [I, 5], assist the instructor in presenting in-class demonstrations [4] and provide hypermedia access to tutorials and demos [2, 3]. Our goal is to provide a self.contained, self-paced learning environment for students of computer graphics. Although our current use of the modules is supplementary to the material presented in formal lectures, we have built the modules with no assumption that the students have had any prior exposure co the concepts. In this way, a module is usable by those who have either missed or not understood the companion lecture, or are not even enrolled in the course. Around-theclock access in our laboratories allows the students to repeat the module unti l they understand the material and provides a useful source for review (e.g., before an exam). Because a module assumes no prior exposure to the topic presented, and because students may use the modules outside of scheduled lab times, progress through the module is deliberately sequential, ensuring that the concepts are presented in a logical order. A user can simply press the Cont(inue) button to step through the explanation and demonstration sections, until such rime as interaction is allowed or required. Modules We are implementing the modules using the C programming language and the Silicon Graphics GL library.The target machines for our use are SGI Indigo X524 workstations. To provide for ease of porting to other hardware and software platforms, we have isolated all of the GL code within our library routines, The following modules have been implemented and are currently being used in our courses: • Windows &Viewports (Figure I) • 2DTransformations (Figures 2 to 5) • Bresenham Line Drawing (Figure 6)

The Image Chip for High Performance 3D Rendering

The Image chip, which accelerates 3D rendering algorithms base on Bresenham's line drawing and Pineda's parallel polygon drawing algorithms, is discussed. With these algorithms, Image can directly ...

The Image chip for high performance 3D rendering

The Image chip, which accelerates 3D rendering algorithms base on Bresenham's line drawing and Pineda's parallel polygon drawing algorithms, is discussed. With these algorithms, Image can directly draw lines, spans, and triangles in wireframe, hidden-line, and Gouraud-shading modes. Image also directly antialiases vectors or provides antialiasing information to enhance antialiasing of vectors or triangles. Image's operation, separation into layers to maximize performance and simplify the input and output interfaces, and support of advanced rendering effects such as Phong shading and texture mapping are described. The designs of Image's internal architecture, host interface, and memory interface are also described.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Design and Performance Evaluation of EXMAN: An EXtended MANchester Data Flow Computer

Data flow computers are high-speed machines in which an instruction is executed as soon as all its operands are available. This paper describes the EXtended MANchester (EXMAN) data flow computer which incorporates three major extensions to the basic Manchester machine. As extensions we provide a multiple matching units scheme, an efficient, implementation of array data structure, and a facility to concurrently execute reentrant routines. A simulator for the EXMAN computer has been coded in the discrete event simulation language, SIMULA 67, on the DEC 1090 system. Performance analysis studies have been conducted on the simulated EXMAN computer to study the effectiveness of the proposed extensions. The performance experiments have been carried out using three sample problems: matrix multiplication, Bresenham's line drawing algorithm, and the polygon scan-conversion algorithm.

Incremental linear interpolation

Two incremental linear interpolation algorithms are derived and analyzed for speed and accuracy. The first is a version of a “simple” digital differential analyzer (DDA) employing fixed-point arithmetic, whereas the second is a new algorithm that uses only integral arithmetic and is a generalization of Bresenham's line-drawing algorithm. The new algorithm is shown to achieve perfect accuracy and, depending on the underlying processor, may be faster than the fixed-point algorithm.